Algebra Examples

$y \leq 4 y > | x - 1 |$

Step 1

Solve $y \leq 4 y$ for $y$ .

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Step 1.1

Move all terms containing $y$ to the left side of the inequality.

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Step 1.1.1

Subtract $4 y$ from both sides of the inequality.

$y - 4 y \leq 0$

Step 1.1.2

Subtract $4 y$ from $y$ .

$- 3 y \leq 0$

Step 1.2

Divide each term in $- 3 y \leq 0$ by $- 3$ and simplify.

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Step 1.2.1

Divide each term in $- 3 y \leq 0$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 y}{- 3} \geq \frac{0}{- 3}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $- 3$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{- 3 y}{- 3} \geq \frac{0}{- 3}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y \geq \frac{0}{- 3}$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Divide $0$ by $- 3$ .

$y \geq 0$

Step 2

Divide each term in $4 y > | x - 1 |$ by $4$ and simplify.

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Step 2.1

Divide each term in $4 y > | x - 1 |$ by $4$ .

$\frac{4 y}{4} > \frac{| x - 1 |}{4}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $4$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{4 y}{4} > \frac{| x - 1 |}{4}$

Step 2.2.1.2

Divide $y$ by $1$ .

$y > \frac{| x - 1 |}{4}$

Step 3

Find the intersection of $y \geq 0$ and $y > \frac{| x - 1 |}{4}$ .

$y \geq 0$ and $y > \frac{| x - 1 |}{4}$

Step 4